The England midfielder joined the Premier League champions on Sunday for a fee believed to be around £12m after spending five seasons at Goodison Park.
However, Royle believes that the 21-year-old could be forced to bide his time in a squad that includes the likes of Yaya Toure, Gareth Barry and Nigel de Jong already occupying the central midfield positions.
"Manchester City have paid for Rodwell's potential," Royle told talkSPORT.
"He's not going to get in the side before Yaya Toure. When you look at the players City have in the position Rodwell plays, there's a lot of competition there with James Milner, Nigel de Jong, David Silva and Gareth Barry all hoping to start.
"He's going to have to stay fit, that has been a problem for him, and pick up the threads of his career because he's never been a regular at Everton."
Rodwell made 51 starts for Everton.